Bayes' theorem

English

Alternative forms

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Etymology

Named after English mathematician Template:W (1701–1761), who developed an early formulation. The modern expression of the theorem is due to Template:W, who extended Bayes's work but was apparently unaware of it.

Proper noun

1. Template:Lb A theorem expressed as an equation that describes the conditional probability of an event or state given prior knowledge of another event.
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Usage notes

The theorem is stated mathematically as:

$P(A\mid B)=\frac{P(B\mid A)P(A)}{P(B)}$,

where $A$ and $B$ are events with $P(B)\ne 0$, and

• $P(A)$ and $P(B)$ are the Template:M of observing $A$ and $B$ without regard to each other.
• The Template:M $P(A\mid B)$ is the probability of observing event $A$ given that $B$ is true.
• Similarly, $P(B\mid A)$ is the probability of observing event $B$ given that $A$ is true.

Synonyms

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Related terms

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See also

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Further reading

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